Posted by **Anonymous** on Thursday, January 19, 2012 at 10:33pm.

the sides of a triangle have lengths 4x+1, 2x+1 and 6x-1. if the lengths of the longest side is 6x-1, what values of x make the triangle obtuse?

- geometry -
**Reiny**, Thursday, January 19, 2012 at 11:52pm
(6x-1)^2 > (4x+1)^2 + (2x+1)^2 ,

36x^2 - 12x + 1 = 16x^2 + 8x + 1 + 4x^2 + 4x + 1

6x^2 - 24x -1 > 0

suppose we solve the corresponding equation

6x^2 - 24x -1 = 0

x = (24 ± √600)/12

=(24 ± 10√6)/24

= (12 ± 5√6)/12 = appr 2.0206 or a negative

but clearly 6x-1 > 0

x > 1/6

so it is obtuse for x > 2.0206

## Answer this Question

## Related Questions

- Math - If all of the following triangles have the same perimeter, which has the ...
- Geometry - 1. The sides of a triangle have lenghts x, x+4, and 20. Specify those...
- geometry inequality triangles help if you can - Two sides of an obtuse triangle ...
- geometry - If a triangle has sides of lengths a and b, which make a C-degree ...
- Geometry - The lengths of the sides of a triangle are 6 cm, 7 cm and 9 cm. In a...
- ALGEBRA - The perimeter of a triangle is 52 centimeters. The longest is 2 ...
- Algebra - The perimeter of a triangle is 52 centimeters. The longest is 2 ...
- Geometry - The sides of a triangle have lengths of 9, 11, and 16 units. What is ...
- math - The lengths of the sides of a triangle are 4in.,14 in., and 16 in.If the...
- math please help - In a triangle, the lengths of the sides are 3,7,and 8. If the...

More Related Questions